Question

Please help I’m not sure how to answer this

Answer 1

• x = 53°
• AB ≈ 18.8 units

Explanation:

You want the measure of angle A and diameter AB for inscribed triangle ADB, given DB = 15 and angle B is 37°.

Triangle ADB

Triangle ADB is inscribed in a semicircle, hence is a right triangle. That means the angle marked x is the complement of angle B:

x = 90° -37°

x = 53°

Cosine

The cosine relation tells you ...

Cos = Adjacent/Hypotenuse

cos(37°) = DB/AB

AB = DB/cos(37°) = 15/cos(37°)

AB ≈ 18.8 . . . . units

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Additional comment

The inscribed angle theorem tells you that arc AD is twice the measure of inscribed angle ABD, so is 74°. The measure of a semicircle (arc ADB) is 180°, so arc DB is 180° -74° = 106°. That means inscribed angle DAB (x) is 106°/2 = 53°.

Of course, once you recognize angle D is half of 180°, a right angle, going directly to finding the complement of angle B is much easier.

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